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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> =  <a href="rfinseq.html#K2" target="_self">MIM</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>
<a NAME="E1:31"/><i><font color="Green">E22</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 
<b>by </b><i><a class="ref" href="rfinseq.html#D3" target="_self">Def3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_1_1"/>
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font> or <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_1"><b>case </b></a><a NAME="E1:31_1_1_1"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><div class="add"><a NAME="E2:31_1_1_1"/><b>then </b>
( <span class="p1">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K1">REAL</a>  &amp; <font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K6">&lt;*&gt;</a> <a href="numbers.html#K1">REAL</a>  )
 <b>by </b><i><a class="txt" href="rfinseq.html#E1:31"><i><font color="Green">E22</font></i></a>, <a class="ref" href="rfinseq.html#D2" target="_self">Def2</a></i>;<br/><b>hence </b><a NAME="E3:31_1_1_1"/>
<span class="p1">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rfinseq.html#K2" target="_self">MIM</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="rfinseq.html#T25" target="_self">Th25</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_2"><b>case </b></a><a NAME="E1:31_1_1_2"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/><div class="add"><a NAME="E2:31_1_1_2"/><b>then </b><i><font color="Green">E24</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="rfinseq.html#E1:31"><i><font color="Green">E22</font></i></a>, <a class="ref" href="rfinseq.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E3:31_1_1_2"/><i><font color="Green">E25</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="rfinseq.html#E1:31_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="rfinseq.html#D2" target="_self">Def2</a></i>;<br/><a NAME="E4:31_1_1_2"/><i><font color="Green">E26</font></i>: 
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="rfinseq.html#D3" target="_self">Def3</a></i>;<br/><a NAME="E5:31_1_1_2"/><i><font color="Green">E27</font></i>: 
(  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> &amp;  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:31_1_1_2_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
 ;<br/><a NAME="E2:31_1_1_2_1"/><b>then </b><i><font color="Green">E29</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="finseq_1.html#T3">FINSEQ_1:3</a></i>;<br/><a NAME="E3:31_1_1_2_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E4:31_1_1_2_1"/><b>then </b><i><font color="Green">E30</font></i>: 
( 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> )
 <b>by </b><i><a class="txt" href="rfinseq.html#E3:31_1_1_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rfinseq.html#E2:31_1_1_2_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a>, <a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><b>set </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><a NAME="E5:31_1_1_2_1"/><i><font color="Green">E31</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rfinseq.html#E1:31_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="rfinseq.html#E5:31_1_1_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="rfinseq.html#E1:31_1_1_2_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="rfinseq.html#D2" target="_self">Def2</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="31_1_1_2_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_2_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:31_1_1_2_1_1_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> or <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_2_1_1_1_1"><b>case </b></a><a NAME="E1:31_1_1_2_1_1_1_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><div class="add"><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="rfinseq.html#E2:31_1_1_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rfinseq.html#E3:31_1_1_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rfinseq.html#E5:31_1_1_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="rfinseq.html#E1:31_1_1_2_1"><i><font color="Green">E28</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="rfinseq.html#E1:31"><i><font color="Green">E22</font></i></a>, <a class="txt" href="rfinseq.html#E3:31_1_1_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rfinseq.html#E1:31_1_1_2_1_1_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="rfinseq.html#D3" target="_self">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="rfinseq.html#E4:31_1_1_2"><i><font color="Green">E26</font></i></a>, <a class="txt" href="rfinseq.html#E5:31_1_1_2_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="rfinseq.html#E1:31_1_1_2_1_1_1_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="rfinseq.html#D3" target="_self">Def3</a></i>
;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="31_1_1_2_1_1_1_2"><b>case </b></a><a NAME="E1:31_1_1_2_1_1_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><div class="add"><a NAME="E2:31_1_1_2_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rfinseq.html#E2:31_1_1_2_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/><a NAME="E3:31_1_1_2_1_1_1_2"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/><a NAME="E4:31_1_1_2_1_1_1_2"/><b>then </b><i><font color="Green">E33</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="rfinseq.html#E3:31_1_1_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="nat_1.html#T29">NAT_1:29</a>, <a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><b>set </b><font color="Maroon">c<sub>8</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/><a NAME="E5:31_1_1_2_1_1_1_2"/><i><font color="Green">E34</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="nat_1.html#K1">+</a> 1
 ;<br/><a NAME="E6:31_1_1_2_1_1_1_2"/><b>then </b><i><font color="Green">E35</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="real_1.html#K5">-</a> 1 &amp; <font color="Maroon">c<sub>6</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> 1 )
 <b>by </b><i><a class="txt" href="rfinseq.html#E3:31_1_1_2_1_1_1_2"><i><font color="Green">E32</font></i></a>, <a class="txt" href="rfinseq.html#E4:31_1_1_2_1_1_1_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="xreal_1.html#T21">XREAL_1:21</a></i>;<br/><a NAME="E7:31_1_1_2_1_1_1_2"/>
1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/><a NAME="E8:31_1_1_2_1_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rfinseq.html#E3:31_1_1_2_1_1_1_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="finseq_3.html#T27">FINSEQ_3:27</a></i>;<br/><a NAME="E9:31_1_1_2_1_1_1_2"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rfinseq.html#E1:31_1_1_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="rfinseq.html#D2" target="_self">Def2</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="rfinseq.html#E2:31_1_1_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rfinseq.html#E3:31_1_1_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rfinseq.html#E5:31_1_1_2"><i><font color="Green">E27</font></i></a>, <a class="txt" href="rfinseq.html#E1:31_1_1_2_1"><i><font color="Green">E28</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="real_1.html#K5">-</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="seq_1.html#K2">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="rfinseq.html#E1:31"><i><font color="Green">E22</font></i></a>, <a class="txt" href="rfinseq.html#E4:31_1_1_2_1"><i><font color="Green">E30</font></i></a>, <a class="txt" href="rfinseq.html#E5:31_1_1_2_1_1_1_2"><i><font color="Green">E34</font></i></a>, <a class="txt" href="rfinseq.html#E6:31_1_1_2_1_1_1_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="rfinseq.html#D3" target="_self">Def3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="rfinseq.html#E1:31"><i><font color="Green">E22</font></i></a>, <a class="txt" href="rfinseq.html#E2:31_1_1_2_1"><i><font color="Green">E29</font></i></a>, <a class="txt" href="rfinseq.html#E5:31_1_1_2_1"><i><font color="Green">E31</font></i></a>, <a class="txt" href="rfinseq.html#E6:31_1_1_2_1_1_1_2"><i><font color="Green">E35</font></i></a>, <a class="txt" href="rfinseq.html#E9:31_1_1_2_1_1_1_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="rfinseq.html#D3" target="_self">Def3</a></i>
;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E7:31_1_1_2_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="seq_1.html#K2">.</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/></div><b>end;</b></div><b>hence </b><a NAME="E7:31_1_1_2"/>
<span class="p1">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rfinseq.html#K2" target="_self">MIM</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="rfinseq.html#E2:31_1_1_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="rfinseq.html#E3:31_1_1_2"><i><font color="Green">E25</font></i></a>, <a class="txt" href="rfinseq.html#E4:31_1_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="finseq_2.html#T10">FINSEQ_2:10</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:31"/>
<span class="p1">(<span class="default"><a href="rfinseq.html#K2" target="_self">MIM</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="rfinseq.html#K2" target="_self">MIM</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="rfinseq.html#K1" target="_self">/^</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/>


</div>
